On the Schrodinger equation for the interaction x²+λx²/(1+gx²)

Abstract

By forming the (6,6) Pade approximants to the energy perturbation series for the interaction x2+ lambda x2/(1+gx2) as obtained from the hypervirial relations, the ground and the first three excited state energy levels are calculated. For g<or=2, the results of the present calculation are in good agreement with those of the variational calculations. The authors also present another set of exact solutions to the Schrodinger equation for the interaction x2+ lambda x2/(1+gx2).